Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#501 ⋊ C2 |
| Sylow | C7 ⋊ #1660 |
196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,c^2=f,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,h^b=h^6,d^c=dg,e^c=efg68 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1660, C2×#11729145, #13334948, … |
| maximal normal subgroup of | D7×#1660, C2×#11729145, #13334948, … |
| maximal quotient of | #13242587, #13242606, #13242623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3911);